It is emphasized that for interactions with derivative couplings, the Ward Identity (WI) securing the preservation of a global symmetry should be modified. Scalar QED is taken as an explicit example. More precisely, it is rigorously shown in scalar QED that the naive WI and the improved Ward Identity (‘Master Ward Identity’, MWI) are related to each other by a finite renormalization of the time-ordered product (‘T-product’) for the derivative fields, and we point out that the MWI has advantages over the naive WI—in particular with regard to the proof of the MWI. We show that the MWI can be fulfilled in all orders of perturbation theory by an appropriate renormalization of the T-product, without conflict with other standard renormalization conditions. Relations with other recent formulations of the MWI are established.

要强调的是，对于与导数耦合的相互作用，应修改确保全局对称性保留的Ward Identity（WI）。标量QED就是一个明确的例子。更准确地说，在标量QED中严格显示，朴素的WI和改进的Ward Identity（“主Ward Identity”，MWI）通过对时间乘积（“ T -product”）进行有限的重新归一化而相互关联。对于微分领域，我们指出MWI比单纯的WI有优势-特别是在MWI的证明方面。我们表明，通过对T进行适当的归一化，可以在所有扰动理论上实现MWI。产品，不与其他标准重归一化条件冲突。建立了与MWI其他最新公式的关系。